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Verified Answer :

\(f(x)=2x-7\to D_f:x\in\mathbb{R}\\\\g(x)=-6x-3\to D_g:x\in\mathbb{R}\\\\f(x)+g(x)=(2x-7)+(-6x-3)=2x-7-6x-3\\\\=(2x-6x)+(-7-3)=-4x-10\to D_{f+g}:x\in\mathbb{R}\)